摘要
借助于数学上的二次型理论,给出一种求解n维坐标与动量耦合的谐振子的普遍方法,并且运用该方法求出了二维和三维坐标与动量耦合的本征值.该方法给出的结论与其他方法相同,说明该方法的正确性,并且由于该方法不需要求出变换矩阵的具体形式,使得运用此方法求解具有对称形式的哈密顿量的本征值问题变得简单,易计算出结果.该方法具有普遍性,是一种十分有效的代数方法.
By means of quadratic theory,we present a general method to solve the energy eigenvalue of coordinate and momentum coupling of n-dimensional harmonic oscillator.To apply this method to solve the energy eigenvalue of two-dimensional and three-dimensional coupling harmonic oscillator,our conclusion is the same with the others.Since the present method does not require a specific form of transformation matrix,this makes it be simple to solve the eigenvalue of a symmetrical form Hamilton and easy to calculate the results.This method is a universal and very effective algebraic method.
出处
《大学物理》
北大核心
2011年第3期11-13,18,共4页
College Physics
关键词
量子光学
n维耦合谐振子
二次型
坐标与动量耦合
能量本征值
对角化
quantum optics
n-dimensional coupled harmonic oscillators
quadratic theory
coordinate and momentum coupling
energy eigenvalue
diagonalization